A family of non-uniform subdivision schemes with variable parameters for curve design

Fang, Meie; Jeong, Byeongseon; Yoon, Jungho

doi:10.1016/j.amc.2017.05.063

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…In fact, there have been works [5,21,22] on the local control, which assigned a parameter to each edge of the initial control polygon. Different from these schemes, the work in [9] assigned a parameter to each initial control point, which can also locally control the limit curves.…”

Section: Discussion On the Local Controlmentioning

confidence: 99%

A Variant Cubic Exponential B-Spline Scheme with Shape Control

Zhang

Zheng

2021

Mathematics

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This paper presents a variant scheme of the cubic exponential B-spline scheme, which, with two parameters, can generate curves with different shapes. This variant scheme is obtained based on the iteration from the generation of exponentials and a suitably chosen function. For such a scheme, we show its C2-convergence and analyze the effect of the parameters on the shape of the generated curves and also discuss its convexity preservation. In addition, a non-uniform version of this variant scheme is derived in order to locally control the shape of the generated curves. Numerical examples are given to illustrate the performance of the new schemes in this paper.

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Section: Discussion On the Local Controlmentioning

confidence: 99%

A Variant Cubic Exponential B-Spline Scheme with Shape Control

Zhang

Zheng

2021

Mathematics

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“…Theorem 20: A refinement scheme (13) reproduces polynomials of degree 1 with respect to the primal parameterizations with τ = 0 if and only if y (k)…”

Section: B Polynomial Generation and Reproductionmentioning

confidence: 99%

“…Mustafa et al [12] introduced the families of interpolating schemes with parameters in 2014. In 2017, Feng et al [13] presented a family of non-uniform schemes with variable parameters. Tan et al [14] presented a new 5-point binary approximating scheme with two parameters in 2017.…”

Section: Introductionmentioning

confidence: 99%

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A Class of Refinement Schemes With Two Shape Control Parameters

et al. 2020

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A subdivision scheme defines a smooth curve or surface as the limit of a sequence of successive refinements of given polygon or mesh. These schemes take polygons or meshes as inputs and produce smooth curves or surfaces as outputs. In this paper, a class of combine refinement schemes with two shape control parameters is presented. These even and odd rules of these schemes have complexity three and four respectively. The even rule is designed to modify the vertices of the given polygon, whereas the odd rule is designed to insert a new point between every edge of the given polygon. These schemes can produce high order of continuous shapes than existing combine binary and ternary family of schemes. It has been observed that the schemes have interpolating and approximating behaviors depending on the values of parameters. These schemes have an interproximate behavior in the case of non-uniform setting of the parameters. These schemes can be considered as the generalized version of some of the interpolating and B-spline schemes. The theoretical as well as the numerical and graphical analysis of the shapes produced by these schemes are also presented.

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“…Another study [26], was proposed for non-uniform subdivision for B-splines of arbitrary degrees; their approach is similar to the Lane-Riensenfeld algorithm that composes the doubled control points. In the following study [27], the subdivision scheme was designed as the generalized B-splines that unifies classic B-splines with algebraic-trigonometric B-splines and algebraic-hyperbolic B-splines.…”

Section: Subdivisionmentioning

confidence: 99%

Multilevel Design for the Interior of 3D Fabrications

Chynybekova

Choi

2019

Symmetry

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This article presents a multilevel design for infill patterns. The method partitions an input model into subareas and each subarea are applied with different scales of infill patterns. The number of subareas can be decided by users. For each subarea, there are different values of the scaling parameter that determines the number of columns and rows of pattern elements, which is useful to change the weight and strength of a certain area by user demands. Subareas can be symmetric or asymmetric to each other depending on the geometry of a 3D model and the application requirements. In each subarea, there are generated symmetric patterns. The proposed method is also applicable to combining different patterns. The aim of our work is to create lightweight 3D fabrications with lighter interior structures to minimize printing materials and supplementary to strengthen thin parts of objects. Our approach allows for the composition of sparse and dense distributions of patterns of interior 3D fabrications in an efficient way so users can fabricate their own 3D designs.

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A family of non-uniform subdivision schemes with variable parameters for curve design

Cited by 9 publications

References 23 publications

A Variant Cubic Exponential B-Spline Scheme with Shape Control

A Variant Cubic Exponential B-Spline Scheme with Shape Control

A Class of Refinement Schemes With Two Shape Control Parameters

Multilevel Design for the Interior of 3D Fabrications

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